1. Field of the Invention
The invention relates to a method for optimal allocation of the bit rate of a data compressor by transform.
It concerns more specifically such an allocation process for a compressor by orthogonal or biorthogonal transformation, in particular a wavelet transformation, used in combination with a scalar quantizer and a lossless entropy coder.
Hereinafter, reference will mainly be made to a wavelet transformation leading to a Multiresolution Analysis (MRA) implemented using digital filters intended to perform a decomposition into subbands. However, the invention is not limited to a wavelet transformation.
It is recalled that an MRA consists in starting from an image in the space domain with a set of image elements, or pixels, and in decomposing this image into subbands in which the vertical, horizontal and diagonal details are represented. Thus there are three subbands per resolution level as indicated in FIG. 1.
FIG. 1 illustrates an MRA on three resolution levels. In this representation, a subband is represented by a block. Thus, the image is first divided into four blocks with three subbands W1,1, W1,2 and W1,3 and a low-frequency representation W1,0 of the initial image. Subband W1,1 contains the horizontal wavelet coefficients; subband W1,2 contains the vertical wavelet coefficients; subband W1,3 contains the diagonal wavelet coefficients and the block W1,0 is called “summary” or low frequencies.
At the next resolution level, the block W1,0 is itself divided into four blocks (one summary and three subbands) W2,0, W2,1, W2,2 and W2,3 and, finally, the block W2,0 is divided into four blocks W3,0, W3,1, W3,2 and W3,3 for the third resolution level. Naturally, a finer division (by increasing the resolution levels) or a coarser division (by reducing the number of resolution levels) can be carried out.
2. Description of the Prior Art
It is known that the wavelet transform is well suited to image compression since it provides strong coefficients when the image exhibits strong local variations in contrast, and weak coefficients in the areas in which the contrast varies slightly or slowly.
It is also known that the probability distribution of a subband can be modeled by a two-parameter unimodal function, centered at the origin, of the generalized Gaussian type:
            G      αβ        ⁡          (      x      )        =            β              2        ⁢                                  ⁢                  αΓ          ⁡                      (                          1              β                        )                                ⁢          ⅇ              -                                                        x              α                                            β                    
where
      Γ    ⁡          (      ξ      )        =            ∫      0              +        ∞              ⁢                  ⅇ                  -          x                    ⁢              x                  ξ          -          1                    ⁢                          ⁢              ⅆ        x            
For certain applications, particularly when the compression data must be transmitted over transmission channels imposing a bit rate, it is necessary to quantize the subband coefficients in an optimal manner by minimizing the total distortion while satisfying a set bit rate.
The known optimum rate allocation methods propose, in general, performing a digital optimization process based on the minimization of a functional linking rate and distortion and controlled by a Lagrange parameter. In this case, an iterative optimization algorithm is employed which is generally very costly in calculation time and therefore cannot be used for real-time applications or for applications with limited calculation resources. Only simplification of these methods enables higher speed, but the price is a degradation in performance.